few_shots: Example:
Problem/activity:
Problem 1
The table below contains single equations in a single variable, single equations in two variables, and pairs of simultaneous equations in two variables. Check the appropriate box to show whether there is no solution, exactly 1 solution, or if there is an infinite number of solutions.
|                                                          | **           No solution          ** | **           Exactly 1 solution          ** | **           Infinite number of solutions          ** |
|----------------------------------------------------------|--------------------------------------|---------------------------------------------|-------------------------------------------------------|
|                       $${9=4x+7}$$                       |                                      |                                             |                                                       |
|                       $${y=3y+5}$$                       |                                      |                                             |                                                       |
|                    $${y={x\over2}}$$                     |                                      |                                             |                                                       |
|                     $${3x+6y-9=0}$$                      |                                      |                                             |                                                       |
|    $${x=y}$$                        $${1.25x=1.25y}$$    |                                      |                                             |                                                       |
| $${9.9=6x+8y}$$                        $${9x=2.5y-8.8}$$ |                                      |                                             |                                                       |
| $${11x-2y=1.5}$$                        $${11x-2y=2.5}$$ |                                      |                                             |                                                       |
Problem 2
Kim has a small container and a large container as shown.
[IMG]
It takes 16 of the small containers to fill the large container. Three small containers leave 1.95 gallons of space in the big container.
What is the size of each of the two containers?


Standard options: 
A. Solve linear equations in one variable.
B. Analyze and solve pairs of simultaneous linear equations.


Thought: The last three rows of the table in the first problem involves solving pairs of simultaneous linear equations. The second word problem can also be represented as two simultaneous linear equations.
Answer: B

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_001392

8
options: Understand the relationship between numbers and quantities; connect counting to cardinality.

Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects.
problem_activity: Narrative
The purpose of this activity is to notice the pattern that when 0 is added to a number, the number stays the same and the pattern that when 1 is added to a number, the total is the next number in the count sequence, or 1 more (MP7).
MLR2 Collect and Display.
Collect the language students use to describe what they notice about the value of the expressions when 0 and 1 are added. Display phrases such as: “When we add 0, the total is the same number that we started with, because nothing was added.” During the synthesis, invite students to borrow language from the display as needed.
Advances: Conversing, Reading
Representation: Internalize Comprehension.
Synthesis: Some students may benefit from reiterating the patterns of adding zero and adding one. Make a connection between the two patterns students should notice. For example, “When you add zero to any number you get the same number because adding zero is adding nothing”, “When you add one to any number the total is the next number in the count sequence, or one more.”
Supports accessibility for: Conceptual Processing, Organization
Launch
Groups of 2
Display student book
“Diego and Mai recorded their addition expressions and their values on this page. What do you notice? What do you wonder?” (They always added 1 or 0. Sometimes the first and last number are the same.)
30 seconds: quiet think time
1 minute: partner discussion
Share and record responses.
Activity
“Which expressions show that 0 were added?” (
\(4 + 0\)
,
\(2 + 0\)
, and
\(8 + 0\)
)
30 seconds: quiet think time
Share responses. Highlight or circle the expressions that show
\(+ 0\)
.
“When you played the game, what did you do when you had to add 0?” (Nothing. Zero means none so none were added.)
30 seconds: quiet think time
1 minute: partner discussion
Share responses.
“What do you notice about the value of the expressions when 0 are added?” (It stays the same.)
1 minute: quiet think time
1 minute: partner discussion
Share responses.
“When we add 0, the total is the same number that we started with, because nothing was added.”
Repeat the steps above with
\(+ 1\)
.
Student Facing
\(4 + 0\)
4
[IMG]
\(2 + 0\)
2
[IMG]
\(8 + 0\)
8
[IMG]
\(3 + 1\)
4
[IMG]
\(9 + 1\)
10
[IMG]
\(1 + 1\)
2
[IMG]
Student Response
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Activity Synthesis
“
\(3 + 0\)
is how many?” (
\(3 + 0\)
is 3.)
“
\(2 + 0\)
is how many?” (
\(2 + 0\)
is 2.)
“How do you know that
\(2 + 0\)
is 2?” (Because we didn’t add any more, so the 2 stayed the same.)
Repeat with
\(2 + 1\)
.


correct_option_index: 0